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Which must be greate than 1?

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by Patrick_GMATFix » Sun Feb 16, 2014 10:09 am
Since we're dealing with positive integers, we can cross multiply to find that p < q. As a result, q/p must be greater than 1 (answer E). The full solution below is taken from the GMATFix App. It discusses each answer choice in detail

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by Brent@GMATPrepNow » Sun Feb 16, 2014 10:15 am
LulaBrazilia wrote:If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

A) √(p/q)
B) p/(p²)
C) p/2q
D) q/(p²)
E) q/p
Given: p/q < 1
Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
Also, since p and q are both positive, we can conclude that 0 < p < q

Which of the following MUST be greater than 1?

IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty test-maker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.

E) q/p
If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
So, the correct answer must be E

----------------------------------------------------------------

ANOTHER APPROACH
The question asks, "Which of the following MUST be greater than 1?"
So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.

A) √(p/q)
Let p = 1 and q = 4 to get: √(1/4) = 1/2
1/2 is NOT greater than 1, so ELIMINATE A

B) p/(p²)
Let p = 2 to get: 2/(2²) = 1/2
1/2 is NOT greater than 1, so ELIMINATE B

C) p/2q
Let p = 1 and q = 2 to get: 1/2(2) = 1/4
1/4 is NOT greater than 1, so ELIMINATE C

D) q/(p²)
Let p = 1 and q = 2 to get: 2/(1²) = 4
4 IS greater than 1, so KEEP D

E) q/p
Let p = 1 and q = 2 to get: 2/1 = 2
2 IS greater than 1, so KEEP E

We have eliminated A, B, and C. So, we must try a DIFFERENT set of values for answer choices D and E.

D) q/(p²)
Let p = 2 and q = 3 to get: 3/(2²) = 3/4
3/4 is NOT greater than 1, so ELIMINATE D

So, the correct answer must be E

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Tue Nov 17, 2015 10:50 am, edited 1 time in total.
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by Abhishek009 » Sun Feb 16, 2014 10:18 am
LulaBrazilia wrote:If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

A) root(p/q)

B) p/(p^2)

C) p/2q

D) q/(p^2)

E) q/p
Plug in some values

p/q < 1 and p and q are positive integers

Let P = 2 and q = 3

p/q = 0.667 < 1

Now check each options matter of just 10 seconds -

A) root(p/q) root 2/3

B) p/(p^2)= 2/4

C) p/2q = 2/6

D) q/(p^2) = 3/4

E) q/p = 3/2 => 1.5 This is the answer...


IMO (E)
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by [email protected] » Sun Feb 16, 2014 9:02 pm
Hi LulaBrazilia,

Every so often, the GMAT offers a question that looks far more complex than it actually is. Each of the other explanations provided in this string is correct. Here's a faster way of looking at it though...

Since P and Q are POSITIVE INTEGERS and P/Q < 1, inverting the fraction will invert the relationship...so Q/P > 1. The question ask which of the 5 options is greater than 1....

That's answer E

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by Priyaranjan » Mon Nov 16, 2015 8:09 pm
In answer choice D, if p=1, q=2, then q/(p²)= 2/1²= 2/1=2 >1
Brent@GMATPrepNow wrote:
LulaBrazilia wrote:If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

A) √(p/q)
B) p/(p²)
C) p/2q
D) q/(p²)
E) q/p
Given: p/q < 1
Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
Also, since p and q are both positive, we can conclude that 0 < p < q

Which of the following MUST be greater than 1?

IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty test-maker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.

E) q/p
If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
So, the correct answer must be E

---------------------------------

ANOTHER APPROACH
The question asks, "Which of the following MUST be greater than 1?"
So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.

A) √(p/q)
Let p = 1 and q = 4 to get: √(1/4) = 1/2
1/2 is NOT greater than 1, so ELIMINATE A

B) p/(p²)
Let p = 2 to get: 2/(2²) = 1/2
1/2 is NOT greater than 1, so ELIMINATE B

C) p/2q
Let p = 1 and q = 2 to get: 1/2(2) = 1/4
1/4 is NOT greater than 1, so ELIMINATE C

D) q/(p²)
Let p = 1 and q = 2 to get: 1/(2²) = 1/4
1/4 is NOT greater than 1, so ELIMINATE D

STOP.
Since we have eliminated A, B, C and D, the correct answer must be E

Cheers,
Brent
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by [email protected] » Tue Nov 17, 2015 10:12 am
Hi Priyaranjan,

You are correct; Brent's example doesn't actually eliminate Answer D. You could use P=2 and Q=3 though - and THAT example would eliminate Answer D.

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by Brent@GMATPrepNow » Tue Nov 17, 2015 10:51 am
Priyaranjan wrote:In answer choice D, if p=1, q=2, then q/(p²)= 2/1²= 2/1=2 >1
Brent@GMATPrepNow wrote:
LulaBrazilia wrote:If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

A) √(p/q)
B) p/(p²)
C) p/2q
D) q/(p²)
E) q/p
Given: p/q < 1
Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
Also, since p and q are both positive, we can conclude that 0 < p < q

Which of the following MUST be greater than 1?

IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty test-maker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.

E) q/p
If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
So, the correct answer must be E

---------------------------------

ANOTHER APPROACH
The question asks, "Which of the following MUST be greater than 1?"
So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.

A) √(p/q)
Let p = 1 and q = 4 to get: √(1/4) = 1/2
1/2 is NOT greater than 1, so ELIMINATE A

B) p/(p²)
Let p = 2 to get: 2/(2²) = 1/2
1/2 is NOT greater than 1, so ELIMINATE B

C) p/2q
Let p = 1 and q = 2 to get: 1/2(2) = 1/4
1/4 is NOT greater than 1, so ELIMINATE C

D) q/(p²)
Let p = 1 and q = 2 to get: 1/(2²) = 1/4
1/4 is NOT greater than 1, so ELIMINATE D

STOP.
Since we have eliminated A, B, C and D, the correct answer must be E

Cheers,
Brent
Nice catch, Priyaranjan!

I have edited my response.

Cheers,
Brent
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